The present invention relates generally to signal processing techniques. More particularly, the invention is concerned with a method and an apparatus for performing signal separation processings and a medium recording the signal separation method in the form of a program executable with a computer.
In recent years, a human interface has been spotlighted according to the progress of computerization of consumer products. Especially, a hands-free operation is preferred in the case of the car navigation system for safety and convenience, so that the expectation is increasing for a speech recognition system within a surrounding noise. As well known, a surrounding noise degrades the performance of speech recognizer dramatically. To overcome this problem, the noise cancellers based on an adaptive algorithm such as LMS are used. Although they are effective when the system between noise source and observation is stable and noise is separately measurable, their performance degrades if measurement of noise is not precise or a transfer system is unstable.
The blind signal separation or blind noise canceller that does not require any reference noise signal, is preferred for these applications. There are several approaches to build blind signal separation systems. Because those alogrithms based on the gradient algorithm for convergence, there is a similar problem on local minimums on cost function. Also, these algorithms use high order statistics, so that the computational load is not small.
In this paper, a new simple signal separation method is proposed, for example. This method separates signals using the information on relative relationship between source signals.
In transmission of signals originating in different signal sources or systems, there may arise such situation that these signals undergo mutual interference or superposition with given amplification factors in the course of transmission to such extent that they can not be discriminated by the receiver, as exemplified by crosstalk phenomenon. For coping with this problem, there has heretofore been known a technique for performing signal separation processing on the received signals with a view to restoring the original signals from the mutually superposed state. With the conventional signal separation technique, the original signals of two discrete signal sources or systems sent through transmission line(s) or channels and received in mutually indiscernible state can certainly be restored approximately to the original sgnals.
For better understanding of the concept underlying the present invention, description will first be made in some detail of the conventional signal separation technique by reference to FIG. 5 of the accompanying drawings which shows in a functional block diagram a typical one of the signal separation apparatuses known heretofore.
The signal separation apparatus shown in FIG. 5 includes a signal separation means or unit and a transmission channel characteristics estimation means or unit. In the figure, reference numeral 1 denotes a first filter element or module of a variable tap coefficient type for performing filtering operation or processing on an input signal received from the transmission path or channel and originating in a first signal source or system (hereinafter referred to as the first input signal) with a given tap coefficient value, numeral 2 denotes a second filter element or module of a variable tap coefficient type for performing filtering operation or processing on an input signal received from the transmission channel and originating in a second signal source or system (hereinafter referred to as the second input signal) with a given tap coefficient value, numeral 3 denotes a difference calculation module for arithmetically determining a difference between the second input signal and the output signal of the first filter module 1, numeral 4 denotes a difference calculation module for arithmetically determining a difference between the first input signal and the output signal of the second filter module 2, numeral 5 denotes a third filter element or module of a variable tap coefficient type for performing filtering operation or processing on the output signal of the difference calculation module 3 with a given tap coefficient value, numeral 6 denotes a fourth filter element or module of a variable tap coefficient type for performing filtering processing on the output signal of the difference calculation module 4 with a given tap coefficient value, numeral 7 denotes a first cross-correlation calculation module for arithmetically determining cross-correlation between the second input signal and the output signal of the difference calculation module 3, numeral 8 denotes a second cross-correlation calculation module for arithmetically determining cross-correlation between the first input signal and the output signal of the difference calculation module 3, numeral 9 denotes a third cross-correlation calculation module for arithmetically determining cross-correlation between the second input signal and the output signal of the difference calculation module 4, numeral 10 denotes a fourth cross-correlation calculation module for arithmetically determining cross-correlation between the first input signal and an output signal of the difference calculation module 4, numeral 11 denotes a first inverse function calculation module for arithmetically determining an inverse function of the output signal of the first cross-correlation calculation module 7, numeral 12 denotes a second inverse function calculation module for arithmetically determining an inverse function of the output signal of the third cross-correlation calculation module 9, numeral 13 denotes a first multiplication module for determining a product of output signals of the first inverse function calculation module 11 and the second cross-correlation calculation module 8, and numeral 14 denotes a second multiplication module for determining a product of the output signals of the second inverse function calculation module 12 and the fourth cross-correlation calculation module 10. As can be seen in FIG. 5, the signal separation unit is comprised of the first and second filter elements or modules 1 and 2, the first and second difference calculation modules 3 and 4 and the third and fourth filter modules 5 and 6, while the transmission channel characteristics estimation unit is constituted by the first to fourth cross-correlation calculation modules 7 to 10, the first and second inverse function calculation modules 11 and 12, and the first and second multiplication modules 13 and 14.
Next, referring to FIG. 6, description will be directed to operation of the conventional signal separation apparatus of the structure shown in FIG. 5.
For convenience of the description, the original signals of two different signal sources or systems are represented in terms of the time-based notation as follows.
s1(t)xe2x80x83xe2x80x83(Exp. 14)
xe2x80x83s2(t)xe2x80x83xe2x80x83(Exp. 15)
The signals mentioned above undergo distortions in the course of transmission through respective transmission channels due to characteristics thereof, which may be represented in terms of the frequency-based notation as follows.
H11(xcfx89)xe2x80x83xe2x80x83(Exp. 16)
H21(xcfx89)xe2x80x83xe2x80x83(Exp. 17)
H12(xcfx89)xe2x80x83xe2x80x83(Exp. 18)
H22(xcfx89)xe2x80x83xe2x80x83(Exp. 19)
Further, the signals transmitted through the transmission channels of the characteristics represented by the expressions Exp.16 to Exp.19 (such as direct path H11(xcfx89) and H22(xcfx89), corss-talk path H21(xcfx89) and H12(xcfx89)) are represented by
x1(t)xe2x80x83xe2x80x83(Exp. 20)
x2(t)xe2x80x83xe2x80x83(Exp. 21)
On the other hand, the first and second input signals supplied to the signal separation unit and the transmission channel characteristics estimation unit are represented by
y1(t)xe2x80x83xe2x80x83(Exp. 22)
xe2x80x83y2(t)xe2x80x83xe2x80x83(Exp. 23)
Furthermore, signals resulting from the Fourier transformation of the above-mentioned signals (Exp. 14 to Exp. 23) are represented as follows.
S1(xcfx89)xe2x80x83xe2x80x83(Exp. 24)
S2(xcfx89)xe2x80x83xe2x80x83(Exp. 25)
X1(xcfx89)xe2x80x83xe2x80x83(Exp. 26)
X2(xcfx89)xe2x80x83xe2x80x83(Exp. 27)
Y1(xcfx89)xe2x80x83xe2x80x83(Exp. 28)
Y2(xcfx89)xe2x80x83xe2x80x83(Exp. 29)
Then, the following expressions Exp.30, Exp.31, Exp.32 and Exp.33 apply valid.                               S          ⁡                      (            ω            )                          =                  [                                                                                          S                    1                                    ⁡                                      (                    ω                    )                                                                                                                                            S                    2                                    ⁡                                      (                    ω                    )                                                                                ]                                    (                  Exp          .                      xe2x80x83                    ⁢          30                )                                          X          ⁡                      (            ω            )                          =                              [                                                                                                      X                      1                                        ⁡                                          (                      ω                      )                                                                                                                                                              X                      2                                        ⁡                                          (                      ω                      )                                                                                            ]                    =                      [                                                                                                                              H                        11                                            ⁡                                              (                        ω                        )                                                              ⁢                                                                  S                        1                                            ⁡                                              (                        ω                        )                                                                                                                                                                                                            H                        22                                            ⁡                                              (                        ω                        )                                                              ⁢                                                                  S                        2                                            ⁡                                              (                        ω                        )                                                                                                                  ]                                              (                  Exp          .                      xe2x80x83                    ⁢          31                )                                          H          ⁡                      (            ω            )                          =                  [                                                                                          H                    11                                    ⁡                                      (                    ω                    )                                                                                                                    H                    12                                    ⁡                                      (                    ω                    )                                                                                                                                            H                    21                                    ⁡                                      (                    ω                    )                                                                                                                    H                    22                                    ⁡                                      (                    ω                    )                                                                                ]                                    (                  Exp          .                      xe2x80x83                    ⁢          32                )                                                                                    Y                ⁡                                  (                  ω                  )                                            =                                                [                                                                                                                                          Y                            1                                                    ⁡                                                      (                            ω                            )                                                                                                                                                                                                                    Y                            2                                                    ⁡                                                      (                            ω                            )                                                                                                                                ]                                =                HS                                                                                        =                                                [                                                                                                                                          H                            11                                                    ⁡                                                      (                            ω                            )                                                                                                                                                                            H                            12                                                    ⁡                                                      (                            ω                            )                                                                                                                                                                                                                    H                            21                                                    ⁡                                                      (                            ω                            )                                                                                                                                                                            H                            22                                                    ⁡                                                      (                            ω                            )                                                                                                                                ]                                ⁡                                  [                                                                                                                                          S                            1                                                    ⁡                                                      (                            ω                            )                                                                                                                                                                                                                    S                            2                                                    ⁡                                                      (                            ω                            )                                                                                                                                ]                                                                                                        =                              [                                                                                                                                                                                        H                              11                                                        ⁡                                                          (                              ω                              )                                                                                ⁢                                                                                    S                              1                                                        ⁡                                                          (                              ω                              )                                                                                                      +                                                                                                            H                              12                                                        ⁡                                                          (                              ω                              )                                                                                ⁢                                                                                    S                              2                                                        ⁡                                                          (                              ω                              )                                                                                                                                                                                                                                                                                                                  H                              21                                                        ⁡                                                          (                              ω                              )                                                                                ⁢                                                                                    S                              1                                                        ⁡                                                          (                              ω                              )                                                                                                      +                                                                                                            H                              22                                                        ⁡                                                          (                              ω                              )                                                                                ⁢                                                                                    S                              2                                                        ⁡                                                          (                              ω                              )                                                                                                                                                                          ]                                                                        (                  Exp          .                      xe2x80x83                    ⁢          33                )            
At this juncture, it is presumed that values which can be represented by the undermentioned expressions Exp.34 and Exp.35 are set as the initial tap coefficient values for the filter modules 1 and 2, respectively, whereon the filtering operation or processing is performed on the first and second input signals. Refer to FIG. 6, step 1.                                           H            21            xe2x80x2                    ⁡                      (            ω            )                                                H            22            xe2x80x2                    ⁡                      (            ω            )                                              (                  Exp          .                      xe2x80x83                    ⁢          34                )                                                      H            12            xe2x80x2                    ⁡                      (            ω            )                                                H            11            xe2x80x2                    ⁡                      (            ω            )                                              (                  Exp          .                      xe2x80x83                    ⁢          35                )            
The difference calculation module 3 is designed to arithmetically determine the difference between the second input signal and the output signal of the first filter module 1, while the difference calculation module 4 is designed to arithmetically determine the difference between the first input signal and the output signal of the second filter module 2. See the step 2 in FIG. 6. In this conjunction, the output signal of the difference calculation module 4 is represented by the undermentioned expression Exp. 36 in the time-based notation with the output signal of the difference circulation module 3 being represented by the undermentioned expression Exp. 37, while they are given by the expressions Exp. 38 and Exp. 39 in terms of the frequency-based notation.
xe2x80x83v1(t)xe2x80x83xe2x80x83(Exp. 36)
v2(t)xe2x80x83xe2x80x83(Exp. 37)
V1(t)xe2x80x83xe2x80x83(Exp. 38)
V2(t)xe2x80x83xe2x80x83(Exp. 39)
The first cross-correlation calculation module 7 is designed to determine the cross-correlation between the second input signal and the output signal of the difference calculation module 3 on the frequency base, the second cross-correlation calculation module 8 determines the cross-correlation between the first input signal and the output signal of the first difference calculation module 3 on the frequency base, the third cross-correlation calculation module 9 determines the cross-correlation between the second input signal and the second output signal of the difference calculation module 4 on the frequency base, and the fourth cross-correlation calculation module 10 is designed to determine cross-correlation between the first input signal and the output signal of the second difference calculation module 4 on the frequency base. See step 3 in FIG. 6. The cross-correlation values as determined through the arithmetic operations mentioned above can be given by the following expressions Exp.40, Exp.41, Exp.42 and Exp.43.
Py2v2(xcfx89)=E[Y2(xcfx89)xc2x7V2(xcfx89)]xe2x80x83xe2x80x83(Exp. 40)
Py1v2(xcfx89)=E[Y1(xcfx89)xc2x7V2(xcfx89)]xe2x80x83xe2x80x83(Exp. 41)
Py2v1(xcfx89)=E[Y2(xcfx89)xc2x7V1(xcfx89)]xe2x80x83xe2x80x83(Exp. 42)
Py1v1(xcfx89)=E[Y1(xcfx89)xc2x7V1(xcfx89)]xe2x80x83xe2x80x83(Exp. 43)
On the other hand, the first inverse function calculation module 11 is designed to determine an inverse function of the output value (see Exp.40) of the first cross-correlation calculation module 7. The inverse function may be given by the undermentioned expression Exp.44. Similarly, the second inverse function calculation module 12 is designed to determine an inverse function of the output value (see Exp.42) of the third cross-correlation calculation module 9. The resulting inverse function may be given by the undermentioned expression Exp.45. Also see step 4 in FIG. 6.
Py2v2xe2x88x921(xcfx89)xe2x80x83xe2x80x83(Exp. 44)
Py2v1xe2x88x921(xcfx89)xe2x80x83xe2x80x83(Exp. 45)
Furthermore, the first multiplication module 13 serves to determine a product of the output signal (see Exp.44) of the first inverse function calculation module 11 and the output signal (see Exp.41) of the second cross-correlation calculation module 8, while the second multiplication module 14 determines the product of the output signal (Exp.45) of the second inverse function calculation module 12 and the output signal (Exp.43) of the fourth cross-correlation calculation module 10 (step 5 in FIG. 6), whereon the respective products (Exp.46, Exp.47) as determined are employed as the estimated values (see Exp.35 and Exp.34) of filter characteristics intrinsic to the transmission lines or channels for thereby updating the filter tap coefficient values of the first filter module 1, the second filter module 2, the third filter module 5 and the fourth filter module 6, respectively, in terms of the time-based notation value. See step 6 in FIG. 6.                                           H            21                    ⁡                      (            ω            )                                                H            22                    ⁡                      (            ω            )                                              (                  Exp          .                      xe2x80x83                    ⁢          46                )                                                      H            12                    ⁡                      (            ω            )                                                H            11                    ⁡                      (            ω            )                                              (                  Exp          .                      xe2x80x83                    ⁢          47                )            
The first filter module 1 and the second filter module 2 perform filtering processings on the first and second input signals (Exp.22 and Exp.23) supplied to the signal separation unit with respective filter tap coefficient values equivalent to the frequency-based notation values derived from the expressions Exp.34 and Exp.35. Step 7 in FIG. 6.
The difference calculation modules 3 determines arithmetically the difference between the second input signal (Exp.23) and the output signal of the filter module 1 while the difference calculation module 4 determines the difference between the first input signal (Exp.22) and the output signal of the filter module 2. Step 8 in FIG. 6.
The third filter module 5 performs filtering processing on the output signal (Exp.36) of the difference calculation module 3 with the tap coefficient value equivalent to the frequency-based notation of the value given by the undermentioned expression Exp.48 while the fourth filter module 6 performs filtering processing on the output signal (Exp.37) of the difference calculation module 4 with the tap coefficient value equivalent to the time-based notation of the value given by the following expression Exp.48. Step 9 in FIG. 6.                     1                  1          -                                                                      H                  12                  xe2x80x2                                ⁡                                  (                  ω                  )                                            ⁢                                                H                  21                  xe2x80x2                                ⁡                                  (                  ω                  )                                                                                                      H                  11                  xe2x80x2                                ⁡                                  (                  ω                  )                                            ⁢                                                H                  22                  xe2x80x2                                ⁡                                  (                  ω                  )                                                                                        (                  Exp          .                      xe2x80x83                    ⁢          48                )            
The conventional signal separation apparatus of the arrangement described above however suffers a problem that the indirect waves (crosstalk components) ascribable to the characteristics parameters represented by the expressions Exp.46 and Exp.47 can not be estimated in the case where zero-points make appearance in the transfer functions (Exp.16 and Exp.19) for the direct wave.
In the light of the state of the art described above, it is an object of the present invention to provide a signal separation methods, apparatuses and signal storage mediums, which enable extracting original signals of two different systems or sources with high quality and fidelity from the signals transferred from transmission channels even when the original signals have been distorted or superposed in the course of transmission.
In view of the above and other objects which will become apparent as the description proceeds, the present invention is directed to a signal separation apparatus for restoring first and second original signals at receiver equipment, even when these signals have undergone mutual interference or superposition with given amplification factors in the course of transmission to the receiver equipment through transmission channels and thus can not straightforwardly be discriminated by a receiver.
According to an aspect of the present invention, there is provided a signal separation apparatus for separating first and second input signals originating in two discrete signal systems at receiver equipment, which apparatus is comprised of a signal separation section and an evaluation function calculation section, wherein the signal separation section includes first and second filter module each of a variable tap coefficient type for performing filtering processing on the first input signal; third and fourth filter modules each of a variable tap coefficient type for performing filtering processing on the second input signal; a first difference calculation module for determining arithmetically difference between outputs of the first and third filter modules, respectively; a second difference calculation module for determining arithmetically difference between outputs of the second and fourth filter modules, respectively; a fifth filter module of a variable tap coefficient type for performing filtering processing on an output signal of the first difference calculation module; and a sixth filter module of a variable tap coefficient type for performing filtering processing on an output signal of the second difference calculation module; and wherein the evaluation function calculation section includes a first autocorrelation calculation module for determining arithmetically an inverse sign value of autocorrelation of an output signal of the fifth filter module; a second autocorrelation calculation module for determining arithmetically an inverse sign value of autocorrelation of the output signal of the sixth filter module, an addition module for adding together output values of the first and second autocorrelation calculation modules; an absolute value calculation module for determining an absolute value of the output value of the addition module; a square calculation module for determining arithmetically a squared value of the absolute value outputted from the absolute value calculation module; and a minimum value decision module for determining characteristics values of said transmission channels to obtain a minimum value from evaluation function values determined arithmetically with respect to optional characteristics values of said transmission channels.
Further, with the teachings of the present invention, there is provided an algorithm system which allows estimation of the indirect waves (crosstalk components) even in the case where the transfer function of the direct wave has zero point(s) and which makes it possible to perform signal separation processings on the two input signals originating in two different signal sources or systems even when the two input signals have been superposed mutually on the way of transmission due to crosstalks and even when the transfer function of the direct wave has the zero point(s).
Thus, according to further aspects of the present invention, there are provided the followings apparatus, methods and recording mediums as recited in claims.
There is provided an apparatus of claim 2, i.e., a signal separation apparatus according to the above-mentioned aspect, wherein said minimum value is selected by said minimum value decision means to determine components xcex8xe2x80x2(xcfx89)xe2x80x94(Exp.1)xe2x80x94and xcfx86xe2x80x2(xcfx89)xe2x80x94(Exp.2)xe2x80x94in a predetermined range delimited by xe2x88x92xcfx80/2 and xcfx80/2 inclusivexe2x80x94(Exp.3)xe2x80x94, whereby the tap coefficients of said filter means are updated in dependence on the selected components xcex8xe2x80x2(xcfx89) and xcfx86xe2x80x2(xcfx89).
There is still provided a method of claim 3, i.e., a method of separating first and second sequence signals input from transmission channels or paths, comprising the steps of:
(a) performing filtering proceedings on said first and second input signals with first, second, third and fourth filter means having respective controllable tap coefficient values in a frequency-based notation;
(b) performing difference calculation processings on output signals of said first filter means and said third filter means by first difference calculation means while performing difference calculation proceedings on output signals of said second filter means and said fourth filter means by second difference calculation means;
(c) performing filtering processing on output signals of said first and second difference calculation means, respectively, by fifth and sixth filter means each with a controllable tap coefficient value given by an undermentioned expression Exp.8;
(d) determining arithmetically an inverse sign value of autocorrelation of the output signal of said fifth filter means by first autocorrelation calculation means while determining arithmetically an inverse sign value of autocorrelation of the output signal of said sixth filter means by second autocorrelation calculation means;
(e) adding together output signals of the first and second autocorrelation calculation means determined values by addition means;
(f) determining arithmetically an absolute value of an output signal of said addition means by absolute value calculation means;
(g) determining arithmetically a square of the output absolute value of said absolute value calculation means by square calculation means;
(h) determining selectively a combination of tap coefficient values of said first, second, third and fourth filter means, respectively, so as to select a minimum evaluation function value in evaluation function values outputs of said square calculation means determined with optional tap coefficient values of said first, second, third and fourth filter means in the frequency-based notation;
(i) performing filtering processings by said first, second, third and fourth filter means with a combination of tap coefficient values determined in said step (h);
(j) performing difference calculation processing on the output signals of said first and third filter means by said first difference calculation means, while performing difference calculation processing on the output signals of said second and fourth filter means by said second difference calculation means; and
(k) performing filtering processings on the output values of said first and second difference calculation means, respectively, by said fifth and sixth filter means each with an updated tap coefficient value,
wherein said updated tap coefficient value mentioned in said step (k) is given by following expression:                     1                                                            α                1                xe2x80x2                            ⁡                              (                ω                )                                      ⁢                                          α                2                xe2x80x2                            ⁡                              (                ω                )                                              -                                                    β                1                xe2x80x2                            ⁡                              (                ω                )                                      ⁢                                          β                2                xe2x80x2                            ⁡                              (                ω                )                                                                        (                  Exp          .                      xe2x80x83                    ⁢          8                )            
where xcex12xe2x80x2(xcfx89)xe2x80x94(Exp.4)xe2x80x94represents the tap coefficient value of said first filter means determined in said step (h),
xe2x88x92xcex21xe2x80x2(xcfx89)xe2x80x94(Exp.5)xe2x80x94represents the tap coefficient value of said second filter means determined in said step (h),
xe2x88x92xcex22xe2x80x2(xcfx89)xe2x80x94(Exp.6)xe2x80x94represents the tap coefficient value of said third filter means determined in step (h),
xcex11xe2x80x2(xcfx89)xe2x80x94(Exp.7)xe2x80x94represents the tap coefficient value of said fourth filter means determined in said step (h).
There is still provided a method of claim 4, i.e., a method of separating first and second sequence signals input from transmission channels or paths, comprising the steps of:
(a) performing filtering processings on said first and second input signals with first, second, third and fourth filter means having respective controllable tap coefficient values in a frequency-based notation;
(b) performing difference calculation processings on output signals of said first filter means and said third filter means by first difference calculation means while performing difference calculation processings on output signals of said second filter means and said fourth filter means by second difference calculation means;
(c) performing filtering processing on output signals of said first and second difference calculation means respectively by fifth and sixth filter means each with a tap controllable coefficient value given by an undermentioned expression Exp.13;
(d) determining arithmetically an inverse sign value of autocorrelation of the output signal of said fifth filter means by first autocorrelation calculation means while determining arithmetically an inverse sign value of autocorrelation of the output signal of said sixth filter means by second autocorrelation calculation means;
(e) adding together output signals of the first and second autocorrelation calculation means determined values by addition means;
(f) determining arithmetically an absolute value of an output signal of said addition means by absolute value calculation means;
(g) determining arithmetically a square of the output absolute value of said absolute value calculation means by square calculation means;
(h) determining selectively a combination of frequency components of tap coefficient values of said first, second, third and fourth filter means, respectively, within a predetermined range given by undermentioned expression Exp.3 so as to select a minimum evaluation function value in evaluation function values outputs of said square calculation means determined with optional tap coefficient values of said first, second, third and fourth filter means in the frequency-based notation;
(i) performing filtering processing by said first, second, third and fourth filter means with a combination of tap coefficient values determined in said step (h);
(j) performing difference calculation processing on the output signals of said first and third filter means by said first difference calculation means, while performing difference calculation processing on the output signals of said second and fourth filter means by said second difference calculation means; and
(k) performing filtering processings on the output values of said first and second difference calculation means, respectively, by said fifth and sixth filter means each with the updated combination of tap coefficient value,
wherein said updated tap coefficient value mentioned in said step (k) is given by the following expression:                     1                              cos            ⁢                          xe2x80x83                        ⁢                                          θ                xe2x80x2                            ⁡                              (                ω                )                                      ⁢            cos            ⁢                          xe2x80x83                        ⁢                                          φ                xe2x80x2                            ⁡                              (                ω                )                                              -                      sin            ⁢                          xe2x80x83                        ⁢                                          θ                xe2x80x2                            ⁡                              (                ω                )                                      ⁢            sin            ⁢                          xe2x80x83                        ⁢                                          φ                xe2x80x2                            ⁡                              (                ω                )                                                                        (                  Exp          .                      xe2x80x83                    ⁢          13                )            
where xcex8xe2x80x2(xcfx89)xe2x80x94(Exp.1)xe2x80x94and xcfx86xe2x80x2(xcfx89)xe2x80x94(Exp.2)xe2x80x94represent the tap coefficient value frequency components
said predetermined range recited in said step (h) is given by from xe2x88x92xcfx80/2 to xcfx80/2, inclusivexe2x80x94(Exp.3),
cos xcfx86xe2x80x2(xcfx89)xe2x80x94(Exp.9)xe2x80x94represents the tap coefficient value of said first filter means determined in said step (h),
xe2x88x92sin xcex8xe2x80x2(xcfx89)xe2x80x94(Exp.10)xe2x80x94represents the tap coefficient value of said second filter means determined in said step (h),
xe2x88x92sin xcfx86xe2x80x2(xcfx89)xe2x80x94(Exp.11)xe2x80x94represents the tap coefficient value of said third filter means determined in said step (h), and
cos xcex8xe2x80x2(xcfx89)xe2x80x94(Exp.12)xe2x80x94represents the tap coefficient value of said fourth filter means determined in said step (h).
There is still provided a medium of claim 5, i.e., a storage medium recording in the form of a program a signal separation method of processing by two-inputs system to separate two original sequence signals subjected to mutual superposition in transmission channel or paths, thereby restoring the original sequence signals, said method comprising steps of:
(a) performing filtering processings on said first and second input signals with first, second, third and fourth filter means having respective controllable tap coefficient values in a frequence-based notation;
(b) performing difference calculation processings on output signals of said first filter means and said third filter means by first difference calculation means while performing difference calculation proceedings on output signals of said second filter means and said fourth filter means by second difference calculation means;
(c) performing filtering processing on output signals of said first and second difference calculation means, respectively, by fifth and sixth filter means each with a controllable tap coefficient value given by an undermentioned expression Exp.8;
(d) determining arithmeitcally an inverse sign value of autocorrelation of the output signal of said fifth filter means by first autocorrelation calculation means while determining arithmetically an inverse sign value of autocorrelation of the output signal of said sixth filter means by second autocorrelation calculation means;
(e) adding together output signals of the first and second autocorrelation calculation determined values by addition means;
(f) determining arithmetically an absolute value of an output signal of said addition means by absolute value calculation means;
(g) determining arithmetically a square of the output absolute value of said absolute value calculation means by square calculation means;
(h) determining selectively a combination of tap coefficient values of said first, second, third and fourth filter means, respectively, so as to select a minimum evaluation function value in evaluation function values outputs of said square calculation means determined with optional tap coefficient values of said first, second, third and fourth filter means in the frequency-based notation;
(i) performing filtering processings by said first, second, third and fourth filter means with a combination of tap coefficient values determined in said step (h);
(j) performing difference calculation processing on the output signals of said first and third filter means by said first difference calculation means, while performing difference calculation processing on the output signals of said second and fourth filter means by said second difference calculation means; and
(k) performing filtering processings on he output values of said first and second difference calculation means, respectively, by said fifth and sixth filter means each with the updated combination of tap coefficient value,
wherein said updated tap coefficient value mentioned in said step (k)is given by following expression:                     1                                                            α                1                xe2x80x2                            ⁡                              (                ω                )                                      ⁢                                          α                2                xe2x80x2                            ⁡                              (                ω                )                                              -                                                    β                1                xe2x80x2                            ⁡                              (                ω                )                                      ⁢                                          β                2                xe2x80x2                            ⁡                              (                ω                )                                                                        (                  Exp          .                      xe2x80x83                    ⁢          8                )            
where xcex12xe2x80x2(xcfx89)xe2x80x94(Exp.4)xe2x80x94represents the tap coefficient value of said first filter means determined in said step (h),
xe2x88x92xcex21xe2x80x2(xcfx89)xe2x80x94(Exp.5)xe2x80x94represents the tap coefficient value of said second filter means determined in said step (h),
xe2x88x92xcex22xe2x80x2(xcfx89)xe2x80x94(Exp.6)xe2x80x94represents the tap coefficient value of said third filter means determined in said step (h),
xcex11xe2x80x2(xcfx89)xe2x80x94(Exp.7)xe2x80x94represents the tap coefficient value of said fourth filter means determined in said step (h).
There is still provided a medium of claim 6, i.e., a storage medium recording in the form of a program a signal separation method of processing by two-inputs system to separate two original sequence signals subjected to mutual superposition in transmission channel or paths, thereby restoring the original sequence signals, said method comprising steps of:
(a) performing filtering processings on said first and second input signals with first, second, third and fourth filter means having respective controllable tap coefficient values in a frequency-based notation;
(b) performing difference calculation processings on output signals of said first filter means and said third filter means by first difference calculation means while performing difference calculation processings on output signals of said second filter means and said fourth filter means by second difference calculation means;
(c) performing filtering processing on output signals of said first and second difference calculation means respectively by fifth and sixth filter means each with a tap controllable coefficient value given by an undermentioned expression Exp.13;
(d) determining arithmetically an inverse sign value of autocorrelation of the output signal of said fifth filter means by first autocorrelation calculation means while determining arithmetically an inverse sign value of autocorrelation of the output signal of said sixth filter means by second autocorrelation calculation means;
(e) adding together output signals of the first and second autocorrelation calculation means determined values by addition means;
(f) determining arithmetically an absolute value of an output signal of said addition means by absolute value calculation means;
(g) determining arithmetically a square of the output absolute value of said absolute value calculation means by square calculation means;
(h) determining selectively a combination of frequency components of tap coefficient values of said first, second, third and fourth filter means, respectively, within a predetermined range given by undermentioned expression Exp.3 so as to select a minimum evaluation function value in evaluation function values outputs of said square calculation means determined with optional tap coefficient values of said first, second, third and fourth filter means in the frequency-based notation;
(i) performing filtering processing by said first, second, third and fourth filter means with a combination of tap coefficient values determined in said step (h);
(j) performing difference calculation processing on the output signals of said first and third filter means by said first difference calculation means, while performing difference calculation processing on the output signals of said second and fourth filter means by said second difference calculation means; and
(k) performing filtering processings on the output values of said first and second difference calculation means, respectively, by said fifth and sixth filter means each with the updated combination of tap coefficient value,
wherein said updated tap coefficient value mentioned in said step (k) is given by the following expression:                     1                              cos            ⁢                          xe2x80x83                        ⁢                                          θ                xe2x80x2                            ⁡                              (                ω                )                                      ⁢            cos            ⁢                          xe2x80x83                        ⁢                                          φ                xe2x80x2                            ⁡                              (                ω                )                                              -                      sin            ⁢                          xe2x80x83                        ⁢                                          θ                xe2x80x2                            ⁡                              (                ω                )                                      ⁢            sin            ⁢                          xe2x80x83                        ⁢                                          φ                xe2x80x2                            ⁡                              (                ω                )                                                                        (                  Exp          .                      xe2x80x83                    ⁢          13                )            
where xcex8xe2x80x2(xcfx89)xe2x80x94(Exp.1)xe2x80x94and xcfx86xe2x80x2(xcfx89)xe2x80x94(Exp.2)xe2x80x94represent the tap coefficient value frequency components
said predetermined range recited in said step (h) is given by from xe2x88x92xcfx80/2 to xcfx80/2, inclusivexe2x80x94(Exp.3),
cos xcfx86xe2x80x2(xcfx89)xe2x80x94(Exp.9)xe2x80x94represents the tap coefficient value of said first filter means determined in said step (h),
xe2x88x92sin xcex8xe2x80x2(xcfx89)xe2x80x94(Exp.10)xe2x80x94represents the tap coefficient value of said second filter means determined in said step (h),
xe2x88x92sin xcfx86xe2x80x2(xcfx89)xe2x80x94(Exp.11)xe2x80x94represents the tap coefficient value of said third filter means determined in said step (h), and
cos xcex8xe2x80x2(xcfx89)xe2x80x94(Exp.12)xe2x80x94represents the tap coefficient value of said fourth filter means determined in said step (h).
The above and other objects, features and attendant advantages of the present invention will more easily be understood by reading the following description of the preferred embodiments thereof taken, only by way of example, in conjunction with the accompanying drawings.